modeling fake missing transverse energy with bayesian neural networks
DESCRIPTION
Silvia Tentindo Florida State University ACAT 11, Brunel University, UK. Modeling Fake Missing Transverse Energy with Bayesian Neural NetwoRkS. Outline. Motivation Modeling Missing Transverse Energy Results Summary and Conclusions. Motivation – PHysics. - PowerPoint PPT PresentationTRANSCRIPT
Silvia TentindoFlorida State University
ACAT 11, Brunel University, UK
Outline
Motivation
Modeling Missing Transverse Energy
Results
Summary and Conclusions
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Missing Transverse Energy @ the LHC Missing Transverse Energy (MET) is an important
observable in many analyses at the LHC: ElectroWeak,
Top, SUSY, Exotica, Higgs, …
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SM Higgs : Production and Decay yields
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Higgs production Total Cross SectionAt LHC (7 TeV)Gluon Gluon ~ 10pb@MH=150GeV
Higgs branching ratios: H->ZZ, H->WWAnd H->bb are dominant at MH=150GeV
Missing Transverse Energy @ the LHC In particular, it is important in searches for the
Standard Model (SM) Higgs boson in the channels:H W,W (l,ν),(l,ν)H Z, Z (l,l) (ν,ν)H Z, Z (l,l) (b,b); (l,l) (j,j)H Z, Z τ,τ
We will focus here on the following channels:
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H → V V → 2l,2ν V =Z,W
SM Higgs Production and Decay
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gluon gluon fusion vector boson fusion
dominant Higgs production mechanism
Higgs decay modes to di-leptons:
H W W -> (l,v),(l,v)
H ->Z Z -> (l,l) (v,v)
MET
H
W
W H
Z
Z
H → ZZ /WW → 2l,2ν
Di-Muon Event Observed by CMS
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muon
MET
pp → H → ZZ→ 2μ,2νA Higgs candidate event:
muon
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transverse plane view
Monte Carlo Simulation of Variables
Detector simulations at the LHC are able to describe accurately most of the variables that characterize an event
For example: Pt transverse momentum simulated vs measured (ATLAS)
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Monte Carlo Simulation of Missing Et
Missing transverse energy is a complex observable. The quality of its measurement depends on: the hermeticity and granularity of the detector, pile up effects, jet multiplicity, etc.
Missing transverse energy comprises both real missing ET from escaping weakly interacting particles as well as fake missing ET
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Missing ET – definition and measurement
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Definition:
Measurement:
MET true
H Z Z (l, l) (v, v)
MAIN BACKGROUNDSIGNAL q q Z (l,l) + Jets
MET fake
€
/ r E = /
r E real + /
r E fake
€
/ r E = − r p Ti
i∑
Fake Missing Et in a typical background event
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p p --> Z (l l) + jets
Monte Carlo simulation of Missing ET
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Missing Et from simulation and data
The present simulation of missing Et is satisfactory,but future conditions from the machine (increasedluminosity, pile up effects, and increased energy) motivate exploringdata driven modeling of missing Et
Modeling Fake Missing Et Use photon + Jets data to model fake missing Et:
--- Photon + jets events are kinematically and topologically similar to Z + jets events
--- The cross section for photon + jets >> cross section for Z + jets--- The energy of the photon is very well measured
C : Use fake missing Et distribution in photon + jets data to model the fake missing Et in Z + jets events
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Pavlunin arXiv:0906.5016v1
a typical Photon + Jet event
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q q Photon + Jets
MET
fake
Photon + jets events are kinematically and topologically similar to Z + jets events
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transverse plane view
a typical Photon + Jet event
Modeling Fake Missing ET
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photon
jets
MET
MET
The Photon pT and the Fake Missing Et (MET) are related
DeltaPHI (Photon, jets) DeltaPHI(MET, jets)
Modeling Fake Missing ET
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photon
jets
METMET
Fake Missing Et vsPt of Photon
Modeling Fake Missing Et by BNN
1 – The Z pt (Photon pt ) and the fake missing Et (MET) are related: p(MET | pT, …). Moreover, the MET could be related to other observables.
2 – The density p(MET | pT) should be the same for
Z + jets and for Photon + jets
3 – Given pZ(pT) of Z , model the fake MET in Z + jets events using
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€
p(MET) = p(MET | pT ) pZ (pT ) dpT∫
Modeling Fake Missing ET with BNN
4 – Use a Bayesian neural network (BNN) to approximate
where U(MET) is a known density (e.g., a uniform).
(MC) training data: MET, pT from photon + jets (target = 1)
MET from U(MET) and pT from photon + jets (target = 0)
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bnn(MET , pT ) =p(MET, pT )
p(MET, pT )+U(MET)p(pT )
METpT
bnn(MET, pT)
Modeling Fake Missing ET with BNN
5 – Then the desired density can be written as:
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p(MET | pT ) =U(MET)bνν(MET, pT )
1−bνν(MET, pT )⎡⎣⎢
⎤⎦⎥
METpT
bnn(MET, pT)
Results of BNN Training
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MET distributions for a fixed bin in photon pT
Results of BNN Training – Closure Test
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MET distribution integrated over photon pT spectrum
Preliminary results of closure test look promising €
p(MET) = p(MET | pT ) pγ (pT ) dpT∫
Summary and Conclusions
As the LHC luminosity increases (and the energy), we expect that the simulation of MET could become harder
We proposed a method to extract the Fake Missing Et spectrum from photon + jets data and approximate it with a Bayesian neural network.
The method could be useful in modeling the Fake Missing Et for Z + jets events, which are the dominant background in the Higgs to 2l, 2v channel.
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Bayesian Neural Networks
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= =
++=
H
j
P
iiijjj xuavbwxf
1 1
tanh),(
y(x,w)
x1
x2
)],(exp[11),(
wxfwxy
+=
bnn(x) =1N
y(x,wi)i=1
N
∑The weights are sampled from aprobability density function defined onthe neural network parameter space
BNN details
Use ~ 15,000 simulated photon + jets events
Use neural networks (NNs) with 2 inputs and 15 hidden nodes
Generate ensemble of NNs with Flexible Bayesian Modeling (FBM) package by Radford Neal
Average over 100 independent NNs
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Modeling Fake Missing ET
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pp → γ + jet
pp → Z /W + jet
Basic Idea: extract fake missing ET distribution from:
Fake Missing ET
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Courtesy ATLAS+CMS
pp → Z+ jetsZ + jets
Fake missing ET (MET) largely due to jetmismeasurements
Z
jet
Expect MET to be aligned or anti-aligned with jet